In general, a disease manifests not from malfunction of individual molecules but from failure of the relevant system or network, which can be considered as a set of interactions or edges among molecules. Thus, instead of individual molecules, networks or edges are stable forms to reliably characterize complex diseases. This paper reviews both traditional node biomarkers and edge biomarkers, which have been newly proposed. These biomarkers are classified in terms of their contained information. In particular, we show that edge and network biomarkers provide novel ways of stably and reliably diagnosing the disease state of a sample. First, we categorize the biomarkers based on the information used in the learning and prediction steps. We then briefly introduce conventional node biomarkers, or molecular biomarkers without network information, and their computational approaches. The main focus of this paper is edge and network biomarkers, which exploit network information to improve the accuracy of diagnosis and prognosis. Moreover, by extracting both network and dynamic information from the data, we can develop dynamical network and edge biomarkers. These biomarkers not only diagnose the immediate pre-disease state but also detect the critical molecules or networks by which the biological system progresses from the healthy to the disease state. The identified critical molecules can be used as drug targets, and the critical state indicates the critical point of disease control. The paper also discusses representative biomarker-based methods.